The incompressible Navier-Stokes equations (REF ) are solved by using a second-order finite-difference method on a staggered grid [1]}, [2]}. The computational domain is then discretised by a fixed, regular, Eulerian grid, and the spatial derivatives are approximated by standard centred difference discretisation, except for the non-linear term, which makes use of a second-order essentially non-oscillatory (ENO) scheme [3]}. As for the viscous term, we use a second-order centred difference scheme. We have used the projection method to handle the incompressibility condition combined with a multigrid iterative method for solving the elliptic pressure Poisson equation [4]}, [5]}. The numerical method uses an additional adaptive Lagrangian grid based on a hybrid front-tracking/level-set method [6]}, [7]} to track the interface location. The geometrical information, the pressure and velocity variables are exchanged between the adaptive Lagrangian mesh and the fixed Eulerian grid following the Immersed Boundary Method of [8]}. The physical elements that form the Lagrangian interface are advected according to \(\rm {d}\mathbf {x}_f/ \rm {d}t =\mathbf {V}\) , where \(\mathbf {V}\)  is the interface velocity interpolated numerically from the fixed Eulerian grid, using a second-order Runge-Kutta method. Finally, the numerical method uses a domain-decomposition technique for its parallelisation and Message Passing Interface (MPI) for exchanging information between adjacent subdomains. More information regarding the full implementation of the numerical method can be found in [7]}, [10]}
